CZ1 EXPONENTS AND SQUARE ROOTS

This eighth grade mathematics lesson focuses on the application of the Pythagorean Theorem, raising expressions to certain powers, and operations with algebraic expressions. It is the second lesson in a unit of work focused on algebraic expressions. The lesson is 45 minutes in duration. The lesson was taped in a gymnasium - a school that specializes in preparing students for university. There are 30 students in the class.

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00:00:04Dan, Dan stop it. So, Stephanie came back, and Hanka is still absent. Any other changes?
00:00:21Good, then today we will start with Pythagorean theorem. Get ready, take your notebook and write today's date, number of the class.
00:00:38So, the number of the class is 30, today's date. So, I'm going to invite up here Marcela Draslerova, come on Marcela.
00:01:00So, Marcela write the problem statement on the board. I would like you to calculate. We have a given rhombus, which has two diagonals.
00:01:15One is 12 centimeters long, the second one seven centimeters. So please Marcela, find out the perimeter of the rhombus. What is the perimeter of this rhombus?
00:01:37Do you need me to turn the light on? Is it better? So Marcela, talk.
00:02:13So, Marcela, explain.
00:02:15(inaudible)
00:02:16So, diagonals are split into halves, with the help of the Pythagorean theorem we'll figure out the length of each side.
00:02:26Sides. Marcela, what kind of shape is it? The rhombus. The attribute of the diagonals you've explained, one point is discovered, is there any other?
00:02:35It's (inaudible).
00:02:37Yes, that too, we would certainly need it.
00:02:42Psst, Dan!
00:02:43Oh, yes. It has all the sides the same.
00:02:44So, I'm not going to count that, because it was heard before here. So, all the sides are the same length, in that case, we can make the picture easier.
00:02:55There, yes.
00:03:18So, Marcela, I'm going to ask you. You've said, you are going to work with it in a right triangle. How do you know, that triangle is right-angled?
00:03:25Specify there, in which one you'd like to work with the problem. One of them, whichever you choose.
00:03:29So, how do you explain or how do you convince us, that this triangle-
00:03:32Because the diagonals are perpendicular to each other.
00:03:35So, you didn't say that before, yes that's correct.
00:03:48So, Marcela, speak out loud so everybody knows what you're writing on the board.
00:03:50Plus (inaudible) divided by two.
00:03:54Yes.
00:03:57A is equal to the second root of 12 divided by two and square the whole formula, plus seven divided by two and square the second formula.
00:04:15So, when you substitute.
00:04:17A is equal to second root of six square.
00:04:27Uh huh.
00:04:28Plus (inaudible), plus three point five.
00:04:39Yes.
00:04:50So, here is the calculator, Marcela.
00:05:04What is it?
00:05:05Twelve point twenty-five.
00:05:06Twelve point twenty-five.
00:05:31Six point, six point eight.
00:05:37Is it rounded to something? So, did you enter it in the calculator correctly, Marcela? What did the calculator show you?
00:05:42Six point eight (inaudible) nine four.
00:05:44Okay, okay, so it's six point, you said eight?
00:05:46Oh, yes. It's six point nine.
00:05:47Good, of what?
00:05:53Centimeters. Yes, yes. Move a little to the side, Marcela. So, look at the first procedure.
00:05:58Do you have the same results? Any problems so far?
00:06:00So, Marcela, what else?
00:06:02(inaudible) is equal.
00:06:04Uh huh.
00:06:10Yes.
00:06:18Marcela, six point nine by, yes, four.
00:06:27So, we'll try it without a calculator, what would it be.
00:06:40It is twenty-seven point six.
00:06:43Yes, it's twenty-seven point six.
00:06:50Okay, Marcela, it was correct, go sit down. So, do you all have the same answer?
00:06:54Yes.
00:06:55Did anyone have a problem? So, Marcela, it's going to be B for you today, because of the basic figure, because the rhombus was not exactly pictured out.
00:07:02And, unfortunately, we cannot count it, because of Dan's suggestion, so Marcela is going to get B.
00:07:09So, let's try the second time, and it would be for Dan. Let's go Dan.
00:07:19So, Dan, I'd like you to calculate. Do you have a chalk? Calculate the length of the diagonal of the parallelepiped.
00:07:30So, write over there, that it's a parallelepiped.
00:07:37So, calculate the length of the body diagonal, when the measurements of the parallelepiped are: three point two decimeters.
00:07:47The second measurement is 46 centimeters, and the third measurement is going to be five point three decimeters.
00:08:00So, what kind of adjustment did you make? Already, yourself?
00:08:02I transferred it.
00:08:03Transferred to centimeters. So, Dan. I'd like to calculate the length of diagonal of this parallelepiped.
00:08:15So, I'm going to make a sketch.
00:08:23A diagonal.
00:08:25I'll inscribe the sides of the parallelepiped (inaudible).
00:08:36And you have to speak out loud so they can hear you all the way here in the back.
00:08:39(inaudible) A (inaudible) B (inaudible) C.
00:08:43And Dan, in this parallelepiped they are not sides, but-
00:08:47The edges, yes.
00:08:48The edges.
00:08:49Now, I'm going to calculate the side A G.
00:08:52A G.
00:08:55Is it going to be the length of the diagonal? Yes. Mark it into the sketch.
00:09:04Okay.
00:09:06And now it's up to you how we're going to calculate it.
00:09:13So, we will separate it on one side to A, B, C and we'll mark it as a right-angled triangle.
00:09:21So, you meant a wall not a side, a wall yes, so walls A, B, C and D we can use.
00:09:22A wall.
00:09:24(inaudible) walls A, B, C, D, (inaudible) a short diagonal to the right.
00:09:37Uh, huh, yes, mark the right angle there, so it's clear.
00:09:41(inaudible)
00:09:44And loud, Dan, you have to speak out loud so we can understand what you're saying.
00:09:46So, these are (inaudible) A (inaudible) B and this is going to be a diagonal, let's call it for example X.
00:09:49Yes.
00:09:51Yes.
00:09:52So now we can easily figure it out, so X equals a root of A squared plus B squared because it's a hypotenuse.
00:10:01Yes.
00:10:03So X equals a root of 32 squared plus 46 squared.
00:10:12Uh huh.
00:10:16So, Dan, take your calculator or over there on the table you can borrow one.
00:10:28So, I'll write it down. It's a root of 1,024 plus 2,016.
00:10:41Uh huh.
00:10:44I'll add it together, so it's a root of 3,140.
00:10:53Yes.
00:10:57And the result is 56.
00:10:59Uh huh, centimeters, good. So, by doing this we calculated what?
00:11:05A wall diagonal.
00:11:08The length of the wall diagonal. Okay, what is next?
00:11:10Now (inaudible).
00:11:12Yes.
00:11:13So, now we get a right-angled triangle A C G.
00:11:17Yes, so draw the triangle again.
00:11:26This is going to be A, this is C and this is G and this is going to be (inaudible) Y.
00:11:31Yes.
00:11:38So you said that the triangle is, Dan, right-angled. So, this is clear.
00:11:40Right-angled.
00:11:44So, this is practically the (inaudible) C, and this the wall diagonal X and we have to calculate the Y.
00:11:54So, Y is equal- because it's a hypotenuse- it's a root of X squared plus C squared.
00:12:03Yes.
00:12:05So Y is equal to the root of 56 squared plus 53 squared, and Y is equal, where is the calculator.
00:12:13Uh huh.
00:12:18So, you borrow this calculator again.
00:12:29So, it's the root of 3,136 plus 2,809, Y equals the root of 5,945.
00:12:49Uh huh.
00:13:01And that is seventy-seven point one, seventy-seven point one centimeters.
00:13:11Yes, Dan, that was correct. So, now the rest of you take a look at it, Dan was just mumbling over here by the blackboard.
00:13:16So you look at it if you have the same answer.
00:13:19So, Dan, before I let you go tell me how many decimeters it would be.
00:13:22Seven point seventy-one decimeters.
00:13:24That's correct, thank you. So, what about the rest of you. Do you have it or anyone found a problem? Is it good?
00:13:31So, Dan is going to get A today.
00:13:34It was without any mistakes. Now it's an assignment for all of you. I'd like you to do this third part each by yourself.
00:13:45Are you finished? May I start?
00:13:48So, write in your notebook: an easel has sides two point five meters long, an easel has two sides two point five meters long.
00:14:03Everybody knows what an easel looks like? Everybody has seen an easel?
00:14:05Two point what?
00:14:07So, an easel has sides two point five meters long. Calculate, calculate, how far, calculate how far they reach, calculate how far they reach.
00:14:27If the ends of the sides touching the ground, if the ends of the sides touching the ground are one point five meters apart from each other.
00:14:43If the ends of the sides touching the ground are one point five meters apart from each other.
00:14:56So, one more time and slowly. We have an easel, they have sides two point five meters long.
00:15:02I'd like to calculate how far they reach, when you know, that the sides are reaching the ground and the two points are one point five meters apart.
00:15:14Everybody knows what an easel looks like? Can you imagine a picture? Katka?
00:15:17Right-angled (inaudible). Right-angled (inaudible).
00:15:20It depends how you mark it for yourself. It's up to you. Make a sketch, mark sides by your choice.
00:15:27Calculate, how far we can climb, when we're going to stand on the top of the easel?
00:16:25And always in your sketch, don't forget to mark what triangle you are using for calculating.
00:16:30And, also realize what each side of the triangle means.
00:16:59So, who's ready? How are we doing?
00:17:09So, it's just George, nobody else? Somebody has the answer? Tomas with George.
00:17:22So, Tomas. Come up here and write it down.
00:17:27Take your notebook with you and get it ready in the back of the blackboard, so we can check it faster.
00:17:32Hide yourself back there, so you don't give a hint to others. Okay, let's hide you over there, and I'll close it behind you.
00:17:51So, who has any answer raise your hand. I'd like to see it before Tomas finishes it up and we'll look at it together. Yes, that's correct.
00:18:00You need to clarify the measurement. Yes, Marcela rounded the total. Yes. Yes.
00:18:07Kamila, what is it? Uh huh, yes. George? Yes. Martina? Yes.
00:18:20You jumped a little too much. Check it out again, Marcela and correct it. You have some kind of numeric mistake there. Look at it.
00:18:26So, where didn't I go so far? Yes. Dan. Yes, Jonas. Do you have anything written? Good.
00:18:34So, who's work haven't I seen? Yes. Yes. Who else? So, Tom, what does it look like back there? Are you done? Can we look at it?
00:18:43So, round it up, Teresa, but yes, it's correct. Yes, that's right. So, where didn't I go? Dado, show me your work. Yes. Yes. Good.
00:18:55So, Tomas, can we take a look? So, I checked out most of your work.
00:19:15So, good Tom, you can sit down. So we have one option how to calculate this assignment. Look at it. Pss. Quiet.
00:19:24And, check it out if you have the same result, or you came up with any other procedure.
00:19:31Does anyone else have another procedure? And what about the result? Is it the same?
00:19:36Yes.
00:19:37So, when I walked around, I found more or less correct answers.
00:19:40We agreed, we're going to have the measurements with one decimal space, so we'll round the answer on two decimal spaces.
00:19:46On two.
00:19:47Somewhere I saw it rounded up to two point four, someone else had it more specific. It really doesn't matter.
00:19:52Most of the time, we'll leave it rounded to two decimal points. So, there was no problem and we all got it.
00:19:56Good, so now I want you to take your homework and we'll go through numeric terms in your homework.
00:20:16So, can we start? Did you find it in your notebooks? So each of you will do one example and we'll go through it really fast and make it right.
00:20:21So, Marcela, you start.
00:20:22Four plus three times two squared, is four plus three times two and that is 16.
00:20:27That is 16. If there is any problem, tell me right away. Zuzko!
00:20:32Four plus three times two squared, that equals four plus six squared is equal to 40.
00:20:39Yes, that is 40, Dan.
00:20:40Four plus three, in parenthesis, times two squared is equal to seven times two squared and that is 28.
00:20:48And that equals 28. Excellent. Petra.
00:20:51Four plus three times two in parenthesis raised to the second power is equal to 100.
00:20:55Is 100. Petra did it very fast. Katka.
00:20:59Four minus three times two squared is equal to four minus 12 and that is minus eight.
00:21:03And that is minus eight. Katka. Take another one.
00:21:06Four minus three times two squared is equal to four minus six squared and that is minus 32.
00:21:13Minus 32. Jonas.
00:21:15Four minus three in parenthesis times two squared is equal to one times four is four.
00:21:21Is equal to four. Martina.
00:21:23Four minus three times two in parenthesis squared is equal to four minus six all raised to the second power and that equals four.
00:21:31And that is four. So, is everything okay? Did you have any problems? Good.
00:21:35So these are numeric terms and I would like to review a few more complicated ones, when there is something more complicated, if not, we'll come up with something.
00:21:44So, we'll start on page 100 in your textbook and I'd like you to figure out the shown assignment two, and we'll also do the example E.
00:21:57And, who's going to be finished before we'll finish on the blackboard.
00:21:59So the next one you can think about is on page 104, problem number four.
00:22:06And that one we'll do from the beginning to the end.
00:22:07So, first we'll start with the E example. Everybody will calculate one example on the blackboard.
00:22:11This week's service person will in the meantime clean what we've already written on the blackboard.
00:22:15And let's go. Each of you, let's do one piece. And Jana's going to start. Come on Jana.
00:22:24So, Jana, five plus three in the parenthesis divided by four squared, yes the end of parenthesis and divided by four squared.
00:22:37So, Jana, talk and explain what you're doing there.
00:22:38So, the parenthesis come first, so it's eight divided by, four by four is 16, is eight divided by 16 minus two.
00:23:05Are you sure Jana? Eight divided by 16. We're dividing eight by 16.
00:23:21What is it? What is it? Jonas?
00:23:22Zero point five.
00:23:23Zero point five, Jana. Be careful, it's the other way around. So, why do you think it should be minus? Where would you get the minus?
00:23:30I don't know.
00:23:31So, there is no minus. Or, anyone has the answer in a different form?
00:23:35One half.
00:23:36One half, of course. So, Jonas, let's do another one. So, you don't have to take your textbook, you just do it.
00:23:42Five minus three divided by the second root of four.
00:23:49So.
00:23:50So, the root of four is two, three divided, so five.
00:23:56Uh huh.
00:24:00So, don't forget it's equal, at the beginning make another one, at the beginning, at the beginning, so.
00:24:06Three divided by two is one point five, five minus one point five is three point five.
00:24:09Yes.
00:24:15Three point five, uh huh. What about you? Do you agree with that? Nobody has a problem. So, let's do another one.
00:24:22So, Jirka Kral is going to take the next one. Come on Jirka.
00:24:28So, Jirka, for you we have five plus, and in the parenthesis three divided by four, the parenthesis squared.
00:24:36So, it's five plus, uh, three divided by four is zero point, uh.
00:24:37Seventy-five.
00:24:47Yes, that is coming, let him be, let him be.
00:24:51Seventy-five, 75.
00:24:54It looks a little weird.
00:24:55Seventy-five.
00:24:57So. Now you tell me, what you're going to do next with the formula when you should raise by two.
00:25:02So, I'm going to raise it by two.
00:25:03How?
00:25:06Similar to the easel.
00:25:07So, Jirka, now calculators are prohibited, I need you to think about it without calculators. How are you going to do it without a calculator?
00:25:13Shh, shh stop that.
00:25:14Well, we'll draw it.
00:25:18No, no, we'll just calculate today not draw.
00:25:23That's because the zero point 75 is not the best form, Jirka.
00:25:27Go back, go back to the three fractioned by four, three divided by four, okay so now I've said that.
00:25:31Fraction.
00:25:35So, yes. So without a calculator we'll try it now.
00:25:45Yes, so. And now we'll know what to do.
00:25:59So, I want you to write it in the form of a single fraction, Jirka. What is this form called?
00:26:04This is a complex fraction.
00:26:06This isn't a complex fraction. How is it called?
00:26:08Mixed.
00:26:09Mixed number, and now I'd like a simple fraction.
00:26:12(inaudible)
00:26:19So, in this form for example, good Jirka. So, do you all have it? Can we do another one? So, Teresa, come to do another one.
00:26:27But when we had the easel we did it differently.
00:26:29Yes, we could have. Yes. So, Teresa, we have for you five minus three in parenthesis, divided by the square root of four and all raised to the second power.
00:26:42Entirely the whole thing, squared.
00:26:50Five minus three is two, divided by the root of four is two and the whole formula squared.
00:26:56Yes.
00:27:00So, it's two divided by two, that is one squared, and that is equal.
00:27:04Which is equal?
00:27:04One.
00:27:05One, that's correct. So, do we all have it? Any problems?
00:27:09So, now I want you to, everyone on your own solve the problem in example number four.
00:27:16What do we have to do there, Martina? Read it.
00:27:18Fill in the blanks the correct answers of signs for bigger and smaller.
00:27:22Bigger, smaller. So, calculate and fill out the correct answer bigger than, smaller than, equal.
00:27:29So, without calculators, without calculators, Petra, your brain needs to work.
00:27:43Martina, Martina, don't sleep. Do you have it? Awesome.
00:28:00So, write down also the answers between, so we can check it out and we can explain why it is that way, not just having the answer written down.
00:28:35So, finish writing and calculating.
00:28:53Dan, look into your notebook, not elsewhere.
00:28:59So, shall we. Raise your hand how we're doing, who's already done? So, one more second and finish writing.
00:29:12So, let's check it out. So, always read the problem statement, tell me the between answers so we're sure that it's correct and check, if your answers are the same.
00:29:20So, Dada, do the first one.
00:29:22So, it's two squared plus two squared is equal to two times two squared, so two squared plus two squared is eight.
00:29:30Eight.
00:29:31And two by two squared is also eight.
00:29:34Yes. So in the A example the answer was equal. Petra.
00:29:37Two squared plus two cubed, oh, I have to do example B, two cubed plus two cubed, is bigger than three times two squared.
00:29:42It doesn't matter
00:29:46So.
00:29:47Because the cube of two plus the cube of two is 18.
00:29:50Sixteen.
00:29:51Sixteen.
00:29:52So, how much is the cube of two, Petra?
00:29:53The cube of two is eight.
00:29:54Eight, so on the left side the answer is 16 and on the right side?
00:29:56Sixteen.
00:29:58And three by two squared is 12.
00:30:01Twelve, so.
00:30:02So the 16 is bigger than 12.
00:30:04The left side is bigger than the right one, Jitka.
00:30:07So, two squared plus two cubed is equal to three by two squared.
00:30:12So, what did you get on the left side?
00:30:13So, it's basically four plus eight which is 12 and three by four is also 12.
00:30:16Yes.
00:30:21So, in example C we have, say it one more time an equal symbol, good, Karin, take another one.
00:30:23An equal symbol.
00:30:26Two cubed plus two squared will be eight plus four.
00:30:28Jirka, stop doing that.
00:30:31Which is 12 and that is smaller than two times two cubed, because it's like two times eight, 16.
00:30:35Which is?
00:30:36Sixteen, so, we all have it, we all know it. So, now I have something more difficult for you.
00:30:41Open your textbook on page 103.
00:30:45Until now you've had the expressions given, so now we're going to try it the other way around.
00:30:48On page 103 it's shown at the beginning how you can translate this numeric expression into words.
00:30:58Let's try it if it's more difficult and we'll express it in words. So, the beginning is very simple.
00:31:04The sum of numbers three and five we'll convert into words how?
00:31:09Three plus five.
00:31:10Three plus five. The difference between numbers four and minus eight?
00:31:14E:00]
00:31:15Four minus minus eight. The product means what, Misa?
00:31:20Multiplying.
00:31:23Multiplying, or by. And quotient?
00:31:23Dividing.
00:31:24Dividing, so these are the basic functions and of course, that's not enough and unfortunately we'll have more difficult ones.
00:31:29So, now we have the more difficult ones here. So, now approximately in the middle of the page look and we have some expressions.
00:31:35And there are also powers and roots. So, now we're going to try to read this example and later on we're going to think about it on our own.
00:31:41So, Andrea, try the first one.
00:31:44A four power of difference of numbers five and three.
00:31:47Now, look next to it how they wrote it down.
00:31:50Five minus three in the parenthesis to the fourth power.
00:31:52So, how do we do it that we have the same process as always? So if we're going to calculate it what do we have to do first?
00:31:59Put it in the parenthesis.
00:32:01First, we have to do the calculation in parenthesis and after that raise it to a certain power.
00:32:03Parenthesis and raise it to a certain power.
00:32:06So it's called the fourth power and after that we talk about the difference.
00:32:12So, what kind of calculating am I starting with in this word expression?
00:32:16With the power.
00:32:18With the power, which means, with the process which we're going to be using for calculating as the last one.
00:32:22The last one.
00:32:24First we have to subtract and when we have the answer, we'll raise it to a certain power, okay?
00:32:27Raise it to a certain power.
00:32:29So, let's try the second one. Be careful so you don't have chaos in it. Teresa.
00:32:35The difference of fourth powers of numbers five and three.
00:32:39So, what are we going to start with? First we should calculate what?
00:32:46First we're going to calculate the fourth power.
00:32:48First we're going to calculate the fourth powers and later the answers we'll subtract.
00:32:51We'll subtract.
00:32:52So, look at the word expressions and it starts with "the difference of fourth power". Do you understand that?
00:32:59Yes.
00:33:00Okay, so let's try another one. Lucko, read the next one.
00:33:03Five multiplied by the sum of the numbers 12 and three.
00:33:04So, if we want to calculate it, first we start with what?
00:33:11First we calculate the parenthesis which is 12 plus three.
00:33:13Twelve plus three and the answer, we multiply it by five.
00:33:16Multiply by five.
00:33:17Look at it how it starts. It's five multiplied by a certain sum.
00:33:21So let's try the last two ones. They are going to be the most difficult ones, because we haven't practiced them yet.
00:33:27Let's try them, Kamco. The one before the last one.
00:33:30The square root of the sum of 11 and seven.
00:33:33And now we'll read the last one so you have something to compare it to, Pepo, what is going to be the last one?
00:33:38The total sum of square roots of numbers 11 and seven.
00:33:40So, now look at it how it's written. When I start saying: second root of the total, so the main part is the big root mark.
00:33:50The root mark.
00:33:51And in the last one you have the sum of the square roots.
00:33:54Square roots.
00:33:55So, be very careful, because it's a play with words how you formulate it and it's up to that how you write it down.
00:34:01So, did you understand that? So, I have prepared an easier version for the beginning and I hope it's going to be fast.
00:34:08Now pass it around to each desk, you'll get one example.
00:34:20You'll be able to do it on your own.
00:34:26So it's not just I want you to write it, I also want you to calculate it. So, let's do the example number three as a first one.
00:34:36So, write it down and at the same time calculate it. So far just the example number three.
00:34:41Go through it, go through it, write it down and calculate it.
00:34:46So, I hope there are not going to be any problems with powers and roots, we'll start with the easier ones.
00:35:40So get the number three ready at this point, we'll check it out and after that we'll go further.
00:36:02Read it very carefully so you don't make a mistake. It's better to read it two times before you write it down.
00:36:23So, how is it going? Who has everything? So, a little longer.
00:37:04So, let's do it. So, always read what you've written down and after that, what the answer is. Katko?
00:37:11The difference of numbers 15 and nine is 15 minus nine is six.
00:37:14And the answer is?
00:37:15It's equal to six. Marketa!
00:37:17Fifteen times nine is 135 and it's a product of numbers 15 and nine.
00:37:20One hundred and thirty...
00:37:21You don't have to read it because you all have it there. So, Dan, read the next one.
00:37:25Sixty-four divided by eight is eight.
00:37:27Sixty-four divided by eight is eight. Karin!
00:37:30Seventeen plus 12 is 29.
00:37:32Twenty-nine. Alino.
00:37:34Fifteen plus two times nine is 33.
00:37:37So, what comes first? Don't forget about it, let's remember it.
00:37:41The multiplication.
00:37:42The multiplication. So, let's do the next one. Jitko!
00:37:46In parenthesis 15 plus nine, the end of parenthesis, times four is equal to 96.
00:37:49Times four.
00:37:53Two times 15 plus nine in parenthesis, plus two times 15 plus nine in parenthesis.
00:38:00So what is the answer?
00:38:01Forty-eight.
00:38:02Are the parenthesis necessary there, or we can get by without them?
00:38:06We have to have them.
00:38:08Yes, we have to have the parenthesis here, so let's move on, Katka.
00:38:11May I ask something?
00:38:13About the multiplying by two. Does it matter if it's in front of or after the parenthesis?
00:38:14Yes.
00:38:17So, Katko, show me what we have here.
00:38:18If I look at the answer it doesn't matter, but it's written differently.
00:38:22So tell me what you have there.
00:38:23Fifteen plus nine in parenthesis by two.
00:38:28So, it's this way or what kind of different version did you want?
00:38:30Two by the whole parenthesis.
00:38:33So.
00:38:34The answer is the same, but if I write it the other way, is there any difference?
00:38:35Yes.
00:38:39How do we explain that the answer has to be the same no matter what way we write it down?
00:38:42Because it's commutative.
00:38:43Multiplying is commutative.
00:38:44It's commutative.
00:38:46Sure, so, where are we? So we have also the last one. Zuzko!
00:38:51Fifteen times two plus nine times two is equal to 48.
00:38:54So, Zuzko, are the parenthesis necessary there? We can do it without and the answer is 48.
00:38:55So this first example was hopefully easy. Without a problem.
00:39:02So now I'd like you to try something with decimal numbers possibly something with fractions, so let's try problem number 10.
00:39:18So, now we can start. You try it by yourselves first and on the blackboard you'll have it for comparison.
00:39:19So, we're going to write it on the blackboard. We'll choose always a couple if we have enough space.
00:39:22First we start with two people and it's going to be Marcela and Micha. Come on girls.
00:39:29I'll try to dictate it for you first. So you should just hear it not see it, and try to write it down.
00:39:34So, it's the product of numbers four and 11 made bigger by the difference of numbers 100 and 37.
00:39:49Made bigger by the difference of numbers 100 and 37.
00:39:53So, I'll read it one more time girls. Listen to it and check it.
00:39:56The product of numbers four and 11 made bigger by the difference of numbers 100 and 37.
00:40:04Marcelo, I started with the product of numbers four and 11. Yes. So, finish calculating.
00:40:26So, girls, you can sit down now. Did you get the same answer?
00:40:30So now we'll try a couple of boys. Jirka with Pepa for example, come on boys.
00:40:38So boys, we made this up for you.
00:40:41From the sum of numbers two point four and five point six, from the sum of numbers two point four and five point six we'll subtract, subtract.
00:40:54The quotient of numbers 42 and six. We'll subtract the quotient of numbers 42 and six.
00:41:04Yes, so you started the right way. Finish calculating it.
00:41:20You can go and sit down now guys. So check it. I'm also going to ask.
00:41:24Look at the blackboard. Pepa used the calculation without the parenthesis at all, Jirka added parenthesis. Are they necessary or not?
00:41:32They are not.
00:41:33No, they are not necessary. That's correct. So let's try example C the third one.
00:41:37So we'll try Petra and Stepanka. Come on girls.
00:41:45So, for you I have: with the difference of numbers three and seven.
00:41:50May I write it with (inaudible)?
00:41:51To the difference of numbers three and seven we add the quotient of numbers five and eight.
00:42:03So, with the difference of numbers three and seven add the quotient of numbers five and eight.
00:42:10Petro there is the quotient of five and eight, do you have it there?
00:42:14Now she does.
00:42:15Now she does.
00:42:16Don't transcribe it into a fraction.
00:42:19You could write it in a fraction form for me. If it's possible do it that way.
00:42:30Into a fraction or into a mixed number?
00:42:33Into a fraction. Make it possible to have it in fraction form.
00:42:51Stepanko, look at the signs.
00:42:58So, Petro, are you checking signs?
00:43:03Minus four plus five eighths.
00:43:14So, Stepanko, minus four point zero is what?
00:43:22How many eighths?
00:43:28So, how many eighths?
00:43:30(inaudible)
00:43:31Four point zero?
00:43:34Four point zero. How many eighths is it?
00:43:42Four whole numbers! One whole number has how many eighths? Shh. Let's be patient a little longer.
00:43:49One whole number has how many eighths?
00:43:51Eight.
00:43:52And four of them?
00:43:54Is thirty-two.
00:43:55So it's minus thirty-two eighths plus five eighths is.
00:43:59Minus 28.
00:44:03Thirty-two without five?
00:44:05Twenty-seven.
00:44:06Twenty-seven eighths, so I have an assignment for you.
00:44:07The rest you finish by yourselves and the last example number six you'll do too. You'll write it down and calculate it.
00:44:14So the (inaudible).
00:44:18The last one? We'll go over the last one next time together. So, thank you and that's it.